# Experimental Investigation on the Vector Characteristics of Concentrated Solar Radiation Flux Map

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Details

#### 2.1. Experimental Method

^{2}. The symbol GV is the gray value of the CCD camera. The symbols a

_{c}and b

_{c}are the fitting coefficients of the CCD camera, respectively.

^{2}. The symbol $\rho}_{\mathrm{S}$ is the reflectivity of the left side surface of the rear target, and it is about 0.8. The symbol ${f}_{\mathrm{S}}$ is the transmittance of the neutral density filter installed at the CCD camera during the measurement. The symbol $G{V}_{\mathrm{S},\left(i,j\right)}$ is the gray value at pixel (i, j) of the image photographed by the CCD camera.

#### 2.2. Experimental Apparatus

^{2}.

_{c}and b

_{c}in Equation (1) are equal to 0.08778 and −0.6112, respectively.

## 3. MCRTM Method Coupled with Experimental CSRF on the Focal Plane

^{9}solar rays were sampled for each case. The flowchart of the MCRTM together with the measured results is shown in Figure 4, where the emission positions and the directions are determined by the measured relative CSRI. The symbol N

_{t}is the total ray number sampled, which is set to 10

^{9}as discussed.

## 4. Measurement Results and Experimental Verification

#### 4.1. Composite Measurement of the CSRF Density Distributions

^{2}, as shown in Figure 5.

^{2}. The relative error of the peak heat flux density between the direct and the indirect measurements is about 3.6%. Because the probe of the heat flux meter is too large compared to a single pixel on the curve, the value recorded by the heat flux meter represents the average gray value of the CCD graph inside the rectangular box.

^{6}W/m

^{2}, B = 2560 m

^{−2}.

#### 4.2. The Directional Characteristics of the CSRF

^{−5}to avoid the saturation of the CCD camera), as shown in Figure 6a.

^{2}. In the other three quadrants, the CSRF distributions are relatively uniformly and low. There is a blue hole in the central region, which means that the heat flux in this region is negligible.

#### 4.3. Influences of the Directional CSRI on Thermal Conditions of the Cavity Receiver

^{2}to 0.1 MW/m

^{2}. The relative error of the CSRF value in Figure 7b and that in Figure 7c is up to 16%. These values prove that the directional CSRI plays an important role in the CSRF images of the cavity receiver. More accurate thermal conditions of solar receivers can be obtained when both the spatial CSRF and the directional CSRI are measured together. It is beneficial to the heat transfer improvement of solar thermal applications.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

a_{c},b_{c} | fitting coefficients of the CCD camera |

GV | gray value of the CCD camera |

f_{s} | transmittance of the neutral density filter |

h_{x} | size of the rear target surface along x axis |

h_{y} | size of the rear target surface along y axis |

I_{s} | concentrated solar radiative intensity(CSRI), W/(m^{2}·sr) |

${{I}^{\prime}}_{\mathrm{S}}$ | Relative CSRI, |

L_{S,(i,j)} | incoming solar radiant intensity of the rear target at grid (i, j), W/m^{2} |

l | spacing between the front and rear target, m |

N_{x} | pixel number of the rear target surface image along x axis |

N_{y} | pixel number of the rear target surface image along y axis |

q_{s} | spatial distribution of the CSRF, w/m^{2} |

x | x-direction coordinate, m |

y | y-direction coordinate, m |

r | emission radius for the solar ray, m |

r_{0} | radius of the CSRF spot, m |

R | correlation coefficient of the fitting functions |

R_{φ}, R_{r}, R_{β}, R_{θ} | random number uniformly distributed between zero and one |

Greek symbols | |

θ | zenith angle |

β | circumferential angle |

ΔA | area of surface element, m^{2} |

ΔΩ | solid angle of surface element, sr |

ΔA_{HM} | area of the horn mouth, m^{2} |

μ | total uncertainty |

μ_{A} | type A uncertainty |

μ_{B} | type B uncertainty |

ρ_{s} | reflectivity of the lambertian target |

Subscripts | |

s | solar radiation |

i, j | surface element |

0 | emission positon |

Abbreviations | |

CSRF | concentrated solar radiation flux |

CSRI | concentrated solar radiative intensity |

MCRTM | Monte-Carlo ray-tracing method |

CCD | Charge coupled Device |

## References

- Ávila-Marín, A.L. Volumetric receivers in solar thermal power plants with central receiver system technology: A review. Sol. Energy
**2011**, 85, 891–910. [Google Scholar] [CrossRef] - Avila-Marin, A.L.; Fernandez-Reche, J.; Martinez-Tarifa, A. Modelling strategies for porous structures as solar receivers in central receiver systems: A review. Renew. Sustain. Energy Rev.
**2019**, 111, 15–33. [Google Scholar] [CrossRef] - Cagnoli, M.; Froio, A.; Savoldi, L.; Zanino, R. Multi-scale modular analysis of open volumetric receivers for central tower CSP systems. Sol. Energy
**2019**, 190, 195–211. [Google Scholar] [CrossRef] - Patil, V.R.; Kiener, F.; Grylka, A.; Steinfeld, A. Experimental testing of a solar air cavity-receiver with reticulated porous ceramic absorbers for thermal processing at above 1000 °C. Sol. Energy
**2021**, 214, 72–85. [Google Scholar] [CrossRef] - Ballestrin, J. A non-water-cooled heat flux measurement system under concentrated solar radiation conditions. Sol. Energy
**2002**, 73, 159–168. [Google Scholar] [CrossRef] - Röger, M.; Herrmann, P.; Ulmer, S.; Ebert, M.; Prahl, C.; Göhring, F. Techniques to Measure Solar Flux Density Distribution on Large-Scale Receivers. J. Sol. Energy Eng.
**2014**, 136, 031013–1–031013–10. [Google Scholar] [CrossRef][Green Version] - Wang, Y.; Liu, Q.; Lei, J.; Liu, F. Design and characterization of the non-uniform solar flux distribution measurement system. Appl. Therm. Eng.
**2019**, 150, 294–304. [Google Scholar] [CrossRef] - Ulmer, S.; Lüpfert, E.; Pfänder, M.; Buck, R. Calibration corrections of solar tower flux density measurements. Energy
**2004**, 29, 925–933. [Google Scholar] [CrossRef] - Krueger, K.R.; Lipinski, W.; Davidson, J.H. Operational performance of the university of minnesota 45 kW
_{e}High-Flux Solar Simulator. J. Sol. Energy Eng.**2013**, 135, 044501.1–044501.4. [Google Scholar] [CrossRef] - Li, J.; Gonzalez-Aguilar, J.; Pérez-Rábago, C.; Zeaiter, H.; Romero, M. Optical analysis of a hexagonal 42kWe high-flux solar simulator. Energy Procedia
**2014**, 57, 590–596. [Google Scholar] [CrossRef] - Sarwar, J.; Georgakis, G.; LaChance, R.; Ozalp, N. Description and characterization of an adjustable flux solar simulator for solar thermal, thermochemical and photovoltaic applications. Sol. Energy
**2014**, 100, 179–194. [Google Scholar] [CrossRef] - Levêque, G.; Bader, R.; Lipiński, W.; Haussener, S. Experimental and numerical characterization of a new 45 kWel multisource high-flux solar simulator. Opt. Express
**2016**, 24, A1360–A1373. [Google Scholar] [CrossRef] [PubMed] - Aichmayer, L.; Wang, W.; Garrido, J.; Laumert, B. Experimental flux measurement of a high-flux solar simulator using a Lambertian target and a thermopile flux sensor. In AIP Conference Proceedings; AIP Publishing LLC: Melville, NY, USA, 2016. [Google Scholar]
- Ballestrín, J.; Monterreal, R. Hybrid heat flux measurement system for solar central receiver evaluation. Energy
**2004**, 29, 915–924. [Google Scholar] [CrossRef] - Xiao, J.; Wei, X.; Gilaber, R.N.; Zhang, Y.; Li, Z. Design and characterization of a high-flux non-coaxial concentrating solar simulator. Appl. Therm. Eng.
**2018**, 145, 201–211. [Google Scholar] [CrossRef] - Xiao, J.; Yang, H.; Wei, X.; Li, Z. A novel flux mapping system for high-flux solar simulators based on the indirect method. Sol. Energy
**2019**, 179, 89–98. [Google Scholar] [CrossRef] - Modest, M. Radiative Heat Transfer; Academic Press: Cambridge, MA, USA, 2003. [Google Scholar]
- Shuai, Y.; Xia, X.L.; Tan, H.P. Radiation performance of dish solar concentrator/cavity receiver systems. Sol. Energy
**2008**, 82, 13–21. [Google Scholar] [CrossRef] - Chen, X.; Xia, X.L.; Liu, H.; Li, Y.; Liu, B. Heat transfer analysis of a volumetric solar receiver by coupling the solar radiation transport and internal heat transfer. Energy Convers. Manag.
**2016**, 114, 20–27. [Google Scholar] [CrossRef] - Ali, M.; Rady, M.; Attia, M.A.; Ewais, E.M. Consistent coupled optical and thermal analysis of volumetric solar receivers with honeycomb absorbers. Renew. Energy
**2020**, 145, 1849–1861. [Google Scholar] [CrossRef] - Garcia, P.; Ferriere, A.; Bezian, J.J. Codes for solar flux calculation dedicated to central receiver system applications—A comparative review. Sol. Energy
**2008**, 82, 189–197. [Google Scholar] [CrossRef][Green Version] - He, Y.L.; Cui, F.Q.; Cheng, Z.D.; Li, Z.Y.; Tao, W.Q. Numerical simulation of solar radiation transmission process for the solar tower power plant_ From the heliostat field to the pressurized volumetric receiver. Appl. Therm. Eng.
**2013**, 61, 583–595. [Google Scholar] [CrossRef] - Daabo, A.M.; Mahmoud, S.; Al-Dadah, R.K. The optical efficiency of three different geometries of a small scale cavity receiver for concentrated solar applications. Appl. Energy
**2016**, 179, 1081–1096. [Google Scholar] [CrossRef][Green Version] - Daabo, A.M.; Ahmad, A.; Mahmoud, S.; Al-Dadah, R.K. Parametric analysis of small scale cavity receiver with optimum shape for solar powered closed Brayton cycle applications. Appl. Therm. Eng.
**2011**, 31, 3377–3386. [Google Scholar] [CrossRef] - Kasaeian, A.; Kouravand, A.; Rad, M.A.V.; Maniee, S.; Pourfayaz, F. Cavity receivers in solar dish collectors: A geometric overview. Renew. Energy
**2021**, 169, 53–79. [Google Scholar] [CrossRef] - Du, S.; He, Y.L.; Yang, W.W.; Liu, Z.B. Optimization method for the porous volumetric solar receiver coupling genetic algorithm and heat transfer analysis. Int. J. Heat Mass Transf.
**2018**, 122, 383–390. [Google Scholar] [CrossRef] - Barreto, G.; Canhoto, P.; Collares-Pereira, M. Three-dimensional CFD modelling and thermal performance analysis of porous volumetric receivers coupled to solar concentration systems. Appl. Energy
**2019**, 252, 113433. [Google Scholar] [CrossRef] - Kribus, A. Optical performance of conical windows for concentrated solar radiation. J. Sol. Energy Eng.
**1994**, 116, 47–52. [Google Scholar] [CrossRef] - Karni, J.; Kribus, A.; Ostraich, B.; Kochavi, E. A high-pressure window for volumetric solar receivers. J. Sol. Energy Eng.
**1998**, 120, 101–107. [Google Scholar] [CrossRef] - Timinger, A.; Spirkl, W.; Kribus, A.; Ries, H. Optimized secondary concentrators for a partitioned central receiver system. Sol. Energy
**2000**, 69, 153–162. [Google Scholar] [CrossRef] - Xia, X.L.; Dai, G.L.; Shuai, Y. Experimental and numerical investigation on solar concentrating characteristics of a sixteen-dish concentrator. Int. J. Hydrogen Energy
**2012**, 37, 18694–18703. [Google Scholar] [CrossRef] - Wang, K.; He, Y.L.; Qiu, Y.; Zhang, Y. A novel integrated simulation approach couples MCRT and Gebhart methods to simulate solar radiation transfer in a solar power tower system with a cavity receiver. Renew. Energy
**2016**, 89, 93–107. [Google Scholar] [CrossRef]

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Dai, G.; Zhuang, Y.; Wang, X.; Chen, X.; Sun, C.; Du, S. Experimental Investigation on the Vector Characteristics of Concentrated Solar Radiation Flux Map. *Energies* **2023**, *16*, 136.
https://doi.org/10.3390/en16010136

**AMA Style**

Dai G, Zhuang Y, Wang X, Chen X, Sun C, Du S. Experimental Investigation on the Vector Characteristics of Concentrated Solar Radiation Flux Map. *Energies*. 2023; 16(1):136.
https://doi.org/10.3390/en16010136

**Chicago/Turabian Style**

Dai, Guilong, Ying Zhuang, Xiaoyu Wang, Xue Chen, Chuang Sun, and Shenghua Du. 2023. "Experimental Investigation on the Vector Characteristics of Concentrated Solar Radiation Flux Map" *Energies* 16, no. 1: 136.
https://doi.org/10.3390/en16010136